Hyperbolic arc-(co)secant

Average Error: 0.0 → 0.3

Time: 1.8s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[\]
2. Using strategy rm

3. Applied add-cube-cbrt 0.1

   \[\leadsto \]

4. Applied *-un-lft-identity 0.1

   \[\leadsto \]

5. Applied times-frac 0.1

   \[\leadsto \]

6. Applied add-cube-cbrt 0.1

   \[\leadsto \]

7. Applied *-un-lft-identity 0.1

   \[\leadsto \]

8. Applied times-frac 0.1

   \[\leadsto \]

9. Applied distribute-lft-out 0.1

   \[\leadsto \]

10. Applied log-prod 0.3

    \[\leadsto \]

11. Simplified 0.3

    \[\leadsto \]

12. Final simplification 0.3

    \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  :precision binary64
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))